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  • 1.
    Fernandes, Ralston
    et al.
    Texas A&M University at Qatar.
    Mousavi, Mahmoud
    Aalto University, Finland.
    El-Borgi, Sami
    University of Carthage, Tunisia.
    Free and forced vibration nonlinear analysis of a microbeam using finite strain and velocity gradients theory2016In: Acta Mechanica, ISSN 0001-5970, E-ISSN 1619-6937, Vol. 227, no 9, p. 2657-2670Article in journal (Refereed)
    Abstract [en]

    A nonlinear finite strain and velocity gradient framework is formulated for the Euler-€Bernoulli beam theory. This formulation includes finite strain and the strain gradient within the strain energy generalization as well as velocity and its gradient within the kinetic energy generalization. Consequently, static and kinetic internal length scales are developed to capture size effects. The governing equation with initial and boundary conditions is obtained using the variational approach. Free and forced vibration of a simply supported nanobeam is studied for different values of static and kinetic length scales using the method of multiple scales.

  • 2.
    Mousavi, Mahmoud
    et al.
    Aalto University, Finland.
    Reddy, J. N.
    Texas A&M University, USA.
    Romanoff, Jani
    Aalto University, Finland.
    Analysis of anisotropic gradient elastic shear deformable plates2016In: Acta Mechanica, ISSN 0001-5970, E-ISSN 1619-6937, Vol. 227, no 12, p. 3639-3656Article in journal (Refereed)
    Abstract [en]

    In this paper, Reddy’s third-order shear deformable plate theory is employed for the analysis of centrosymmetric anisotropic plate structures within strain gradient elasticity. The general three-dimensional anisotropic gradient theory is reduced to a two-dimensional formulation for the analysis of thick plate structures. The third-order shear deformation theory (TSDT) takes into account quadratic variation of the transverse shear strains of the plate and does not require shear correction factors. In order to investigate the case of small strains but moderate rotations, the von Kármán strains are considered. The TSDT is also simplified to anisotropic Kirchhoff plate theory within gradient elasticity. To study specific material properties in more detail, the (Kirchhoff and TSDT) gradient plate theory of general anisotropy is simplified to the more practical case of orthotropic plates. It is observed that the gradient theory provides the capability to capture the size effects in anisotropic plate structures. As case studies, the bending and buckling behaviors of the simply supported orthotropic (Kirchhoff and TSDT) plates are studied. Variationally consistent boundary conditions are also discussed. Finally, analytical solutions are presented for the bending and buckling of simply supported orthotropic Kirchhoff plates. The effects of internal length scales on deflections and buckling loads are presented.

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